Pith Number

pith:OMM7TXM4

pith:2026:OMM7TXM4CQTDD7X36HBADHXD5H

not attested not anchored not stored refs pending

The Spectral Dynamics and Noise Geometry of Muon

Mahmoud Abdelmoneum, Pierfrancesco Beneventano, Tomaso Poggio

arxiv:2606.08388 v1 · 2026-06-07 · cs.LG · math.OC · stat.ML

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OMM7TXM4CQTDD7X36HBADHXD5H}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-06-09T01:05:35.379118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7319f9dd9c142631fefbf1c2019ee3e9f51b6788b2b6ddadf1d351308a14ac1a

Aliases

arxiv: 2606.08388 · arxiv_version: 2606.08388v1 · doi: 10.48550/arxiv.2606.08388 · pith_short_12: OMM7TXM4CQTD · pith_short_16: OMM7TXM4CQTDD7X3 · pith_short_8: OMM7TXM4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OMM7TXM4CQTDD7X36HBADHXD5H \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7319f9dd9c142631fefbf1c2019ee3e9f51b6788b2b6ddadf1d351308a14ac1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a12f941f436f5a717e2c6674354b0da947d867e99da9282e0ab23a1e87ee009e",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-07T00:51:30Z",
    "title_canon_sha256": "c4336d6df303b887a5dac0db2ff24a0d6e1b0f1582bcbb415f43089176411b78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08388",
    "kind": "arxiv",
    "version": 1
  }
}